Theorem sylbb2

Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 21-Apr-2019)

	Ref	Expression
Hypotheses	sylbb2.1	⊢ ( 𝜑 ↔ 𝜓 )
	sylbb2.2	⊢ ( 𝜒 ↔ 𝜓 )
Assertion	sylbb2	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		sylbb2.1	⊢ ( 𝜑 ↔ 𝜓 )
2		sylbb2.2	⊢ ( 𝜒 ↔ 𝜓 )
3	2	biimpri	⊢ ( 𝜓 → 𝜒 )
4	1 3	sylbi	⊢ ( 𝜑 → 𝜒 )